The study of maximal gaps between consecutive primes is an important subject that is actively pursued and the Bertrand's postulate [1]} is one of its first consequences. In 1850, Chebyshev proved the Bertrand’s postulate [2]}, and P. Erdös presented a simplified proof in 1932 [3]}. Strong results were also obtained in the generalizations of Bertrand's Postulate. In 2006, M. El Bachraoui proved the existence of a prime in the interval \([2n, 3n]\)  [4]}. In 2011, Andy Loo exhibited a proof that shows not only the existence of a prime between \(3n\)  and \(4n\) , but also the infinitude of the number of primes in this interval when \(n\)  goes to infinity [5]}. Pierre Dusart gave the best known result in this category when he improved in 2016 his previous work by showing that there is a prime between \(x\)  and \((x+x/(25{\log }^2 x))\)  for \(x\ge 468991632\)  [6]}.
